Question
Answer
$$2(4x-1)-(2x-5)(2x+5)=-4x^2+8x+23$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(4x-1)-(2x-5)(2x+5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}8x-2-(4x^2+10x-10x-25) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}8x-2-(4x^2-25) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}8x-2-4x^2+25 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-4x^2+8x+23\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2} $ by $ \left( 4x-1\right) $ $$ \color{blue}{2} \cdot \left( 4x-1\right) = 8x-2 $$ Multiply each term of $ \left( \color{blue}{2x-5}\right) $ by each term in $ \left( 2x+5\right) $. $$ \left( \color{blue}{2x-5}\right) \cdot \left( 2x+5\right) = 4x^2+ \cancel{10x} -\cancel{10x}-25 $$ |
| ② | Combine like terms: $$ 4x^2+ \, \color{blue}{ \cancel{10x}} \, \, \color{blue}{ -\cancel{10x}} \,-25 = 4x^2-25 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 4x^2-25 \right) = -4x^2+25 $$ |
| ④ | Combine like terms: $$ 8x \color{blue}{-2} -4x^2+ \color{blue}{25} = -4x^2+8x+ \color{blue}{23} $$ |
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